TEL AVIV—An Israeli government watchdog on Tuesday released a highly critical report into Prime Minister Benjamin Netanyahu’s travel expenses while he was finance minister more than a decade ago, and raised the possibility of a criminal investigation.

In the report, State Comptroller Yosef Shapira said Mr. Netanyahu had failed to tell a parliamentary committee that numerous trips he and family members took between 2003 and 2005 were paid for by private individuals and organizations. Those payments created the appearance...